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This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in Rn can be efficien...
We propose a class of hierarchical generalized linear models (HGLMs) with random dispersions in this paper, and focus on the properties of the L-N estimators for the fixed effect β in the extended Po...
Meteorological numerical weather prediction (NWP) models solve a system of partial differential equations in time and space.
Abstract: We prove that any unitary representation of GL(n;R) and GL(n;C) admits an equivariant linear form with respect to one of the subgroups considered by Klyachko.
Abstract: In this article, we consider permutation orbifold models of $C_2$-cofinite vertex operator algebras of CFT type. We show the $C_2$-cofiniteness of the 2-cyclic permutation orbifold model $(V...
This paper surveys recent work in applying ideas from graphical models and message passing algorithms to solve large scale regularized regression problems. In particular, the focus is on compressed s...
This paper is devoted to the global (in time) regularity problem for a family of active scalar equations with fractional dissipation. Each component of the velocity field $u$ is determined by the act...
We study graphical representations for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz a...
This paper deals with recovering an unknown vector $\theta$ from the noisy data $Y=A\theta+\sigma\xi$, where $A$ is a known $(m\times n)$-matrix and $\xi$ is a white Gaussian noise. It is assumed tha...
In this survey paper we give a relatively simple and coordinate free description of the WZW model as a local system whose base is the Gm-bundle associated to the determinant bundle on the moduli stack...
Will the cosmological multiverse, when described mathematically,have easily stated properties that are impossible to prove or disprove using mathematical physics? We explore this question by construct...
We examine the long-term asymptotic behavior of dissipating solutions to aggregation equations and Patlak-Keller-Segel models with degenerate power-law and linear diffusion. The purpose of this work...
If G is a finite ℓ-group acting on an affine space An over a finite field K of cardinality prime to ℓ, Serre [29] shows that there exists a rational fixed point. We generalize this to the ...

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